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-revision 1.8 by molod,
Thu Jul 14 19:18:02 2005 UTC
+revision 1.19 by jmc,
Mon Aug 30 23:09:21 2010 UTC
 Line 1
- \section{Fizhi: High-end Atmospheric Physics}
+ \subsection{Fizhi: High-end Atmospheric Physics}
  \label{sec:pkg:fizhi}
  \begin{rawhtml}
  <!-- CMIREDIR:package_fizhi: -->
  \end{rawhtml}
  \input{texinputs/epsf.tex}
- \subsection{Introduction}
+ \subsubsection{Introduction}
  The fizhi (high-end atmospheric physics) package includes a collection of state-of-the-art
  physical parameterizations for atmospheric radiation, cumulus convection, atmospheric
- boundary layer turbulence, and land surface processes.
+ boundary layer turbulence, and land surface processes. The collection of atmospheric
+ physics parameterizations were originally used together as part of the GEOS-3
+ (Goddard Earth Observing System-3) GCM developed at the NASA/Goddard Global Modelling
+ and Assimilation Office (GMAO).
  % *************************************************************************
  % *************************************************************************
- \subsection{Equations}
+ \subsubsection{Equations}
- \subsubsection{Moist Convective Processes}
+ Moist Convective Processes:
  \paragraph{Sub-grid and Large-scale Convection}
  \label{sec:fizhi:mc}
  Sub-grid scale cumulus convection is parameterized using the Relaxed Arakawa
- Schubert (RAS) scheme of Moorthi and Suarez (1992), which is a linearized Arakawa Schubert
+ Schubert (RAS) scheme of \cite{moorsz:92}, which is a linearized Arakawa Schubert
  type scheme.  RAS predicts the mass flux from an ensemble of clouds.  Each subensemble is identified
  by its entrainment rate and level of neutral bouyancy which are determined by the grid-scale properties.
-Line 33 
 buoyancy. RAS assumes that the normalize
+Line 36 
 buoyancy. RAS assumes that the normalize
  mass flux, is a linear function of height, expressed as:
  \[
  \pp{\eta(z)}{z} = \lambda \hspace{0.4cm}or\hspace{0.4cm} \pp{\eta(P^{\kappa})}{P^{\kappa}} =
- -{c_p \over {g}}\theta\lambda
+ -\frac{c_p}{g}\theta\lambda
  \]
  where we have used the hydrostatic equation written in the form:
  \[
- \pp{z}{P^{\kappa}} = -{c_p \over {g}}\theta
+ \pp{z}{P^{\kappa}} = -\frac{c_p}{g}\theta
  \]
  The entrainment parameter, $\lambda$, characterizes a particular subensemble based on its
  detrainment level, and is obtained by assuming that the level of detrainment is the level of neutral
  buoyancy, ie., the level at which the moist static energy of the cloud, $h_c$, is equal
- to the saturation moist static energy of the environment, $h^*$.  Following Moorthi and Suarez (1992),
+ to the saturation moist static energy of the environment, $h^*$.  Following \cite{moorsz:92},
  $\lambda$ may be written as
  \[
- \lambda = { {h_B - h^*_D} \over { {c_p \over g} {\int_{P_D}^{P_B}\theta(h^*_D-h)dP^{\kappa}}} } ,
+ \lambda = \frac{h_B - h^*_D}{ \frac{c_p}{g} \int_{P_D}^{P_B}\theta(h^*_D-h)dP^{\kappa}},
  \]
  where the subscript $B$ refers to cloud base, and the subscript $D$ refers to the detrainment level.
-Line 57 
 rate of change of cumulus kinetic energy
+Line 60 
 rate of change of cumulus kinetic energy
  related to the buoyancy, or the difference
  between the moist static energy in the cloud and in the environment:
  \[
- A = \int_{P_D}^{P_B} { {\eta \over {1 + \gamma} }
+ A = \int_{P_D}^{P_B} \frac{\eta}{1 + \gamma}
- \left[ {{h_c-h^*} \over {P^{\kappa}}} \right] dP^{\kappa}}
+ \left[ \frac{h_c-h^*}{P^{\kappa}} \right] dP^{\kappa}
  \]
- where $\gamma$ is ${L \over {c_p}}\pp{q^*}{T}$ obtained from the Claussius Clapeyron equation,
+ where $\gamma$ is $\frac{L}{c_p}\pp{q^*}{T}$ obtained from the Claussius Clapeyron equation,
  and the subscript $c$ refers to the value inside the cloud.
-Line 69 
 To determine the cloud base mass flux, t
+Line 72 
 To determine the cloud base mass flux, t
  the clouds} is assumed to approximately balance the rate of change of $A$ {\em due to the generation
  by the large scale}. This is the quasi-equilibrium assumption, and results in an expression for $m_B$:
  \[
- m_B = {{- \left.{dA \over dt} \right|_{ls}} \over K}
+ m_B = \frac{- \left. \frac{dA}{dt} \right|_{ls}}{K}
  \]
  where $K$ is the cloud kernel, defined as the rate of change of the cloud work function per
-Line 87 
 and moisture budget equations to determi
+Line 90 
 and moisture budget equations to determi
  temperature (through latent heating and compensating subsidence) and moisture (through
  precipitation and detrainment):
  \[
- \left.{\pp{\theta}{t}}\right|_{c} = \alpha { m_B \over {c_p P^{\kappa}}} \eta \pp{s}{p}
+ \left.{\pp{\theta}{t}}\right|_{c} = \alpha \frac{ m_B}{c_p P^{\kappa}} \eta \pp{s}{p}
  \]
  and
  \[
- \left.{\pp{q}{t}}\right|_{c} = \alpha { m_B \over {L}} \eta (\pp{h}{p}-\pp{s}{p})
+ \left.{\pp{q}{t}}\right|_{c} = \alpha \frac{ m_B}{L} \eta (\pp{h}{p}-\pp{s}{p})
  \]
- where $\theta = {T \over P^{\kappa}}$, $P = (p/p_0)$, and $\alpha$ is the relaxation parameter.
+ where $\theta = \frac{T}{P^{\kappa}}$, $P = (p/p_0)$, and $\alpha$ is the relaxation parameter.
  As an approximation to a full interaction between the different allowable subensembles,
  many clouds are simulated frequently, each modifying the large scale environment some fraction
-Line 101 
 $\alpha$ of the total adjustment. The pa
+Line 104 
 $\alpha$ of the total adjustment. The pa
  towards equillibrium.
  In addition to the RAS cumulus convection scheme, the fizhi package employs a
- Kessler-type scheme for the re-evaporation of falling rain (Sud and Molod, 1988), which
+ Kessler-type scheme for the re-evaporation of falling rain (\cite{sudm:88}), which
  correspondingly adjusts the temperature assuming $h$ is conserved. RAS in its current
  formulation assumes that all cloud water is deposited into the detrainment level as rain.
  All of the rain is available for re-evaporation, which begins in the level below detrainment.
-Line 133 
 Convective cloud fractions produced by R
+Line 136 
 Convective cloud fractions produced by R
  detrained liquid water amount given by
  \[
- F_{RAS} = \min\left[ {l_{RAS}\over l_c}, 1.0 \right]
+ F_{RAS} = \min\left[ \frac{l_{RAS}}{l_c}, 1.0 \right]
  \]
  where $l_c$ is an assigned critical value equal to $1.25$ g/kg.
  A memory is associated with convective clouds defined by:
  \[
- F_{RAS}^n = \min\left[ F_{RAS} + (1-{\Delta t_{RAS}\over\tau})F_{RAS}^{n-1}, 1.0 \right]
+ F_{RAS}^n = \min\left[ F_{RAS} + (1-\frac{\Delta t_{RAS}}{\tau})F_{RAS}^{n-1}, 1.0 \right]
  \]
  where $F_{RAS}$ is the instantanious cloud fraction and $F_{RAS}^{n-1}$ is the cloud fraction
-Line 151 
 Large-scale cloudiness is defined, follo
+Line 154 
 Large-scale cloudiness is defined, follo
  humidity:
  \[
- F_{LS} = \min\left[ { \left( {RH-RH_c \over 1-RH_c} \right) }^2, 1.0 \right]
+ F_{LS} = \min\left[ { \left( \frac{RH-RH_c}{1-RH_c} \right) }^2, 1.0 \right]
  \]
  where
-Line 159 
 where
+Line 162 
 where
  \bqa
  RH_c & = & 1-s(1-s)(2-\sqrt{3}+2\sqrt{3} \, s)r \nonumber \\
     s & = & p/p_{surf} \nonumber \\
-    r & = & \left( {1.0-RH_{min} \over \alpha} \right) \nonumber \\
+    r & = & \left( \frac{1.0-RH_{min}}{\alpha} \right) \nonumber \\
  RH_{min} & = & 0.75 \nonumber \\
  \alpha & = & 0.573285 \nonumber  .
  \eqa
  These cloud fractions are suppressed, however, in regions where the convective
  sub-cloud layer is conditionally unstable.  The functional form of $RH_c$ is shown in
- Figure (\ref{fig:fizhi:rhcrit}).
+ Figure (\ref{fig.rhcrit}).
  \begin{figure*}[htbp]
    \vspace{0.4in}
-   \centerline{  \epsfysize=4.0in  \epsfbox{part6/rhcrit.ps}}
+   \centerline{  \epsfysize=4.0in  \epsfbox{s_phys_pkgs/figs/rhcrit.ps}}
    \vspace{0.4in}
    \caption  [Critical Relative Humidity for Clouds.]
              {Critical Relative Humidity for Clouds.}
-   \label{fig:fizhi:rhcrit}
+   \label{fig.rhcrit}
  \end{figure*}
  The total cloud fraction in a grid box is determined by the larger of the two cloud fractions:
-Line 186 
 F_{CLD} = \max \left[ F_{RAS},F_{LS} \ri
+Line 189 
 F_{CLD} = \max \left[ F_{RAS},F_{LS} \ri
  Finally, cloud fractions are time-averaged between calls to the radiation packages.
- \subsubsection{Radiation}
+ Radiation:
  The parameterization of radiative heating in the fizhi package includes effects
  from both shortwave and longwave processes.
-Line 221 
 The solar constant value used in the pac
+Line 224 
 The solar constant value used in the pac
  and a $CO_2$ mixing ratio of 330 ppm.
  For the ozone mixing ratio, monthly mean zonally averaged
  climatological values specified as a function
- of latitude and height (Rosenfield, et al., 1987) are linearly interpolated to the current time.
+ of latitude and height (\cite{rosen:87}) are linearly interpolated to the current time.
  \paragraph{Shortwave Radiation}
-Line 231 
 heating due to the absoption by water va
+Line 234 
 heating due to the absoption by water va
  clouds, and aerosols and due to the
  scattering by clouds, aerosols, and gases.
  The shortwave radiative processes are described by
- Chou (1990,1992). This shortwave package
+ \cite{chou:90,chou:92}. This shortwave package
  uses the Delta-Eddington approximation to compute the
  bulk scattering properties of a single layer following King and Harshvardhan (JAS, 1986).
  The transmittance and reflectance of diffuse radiation
- follow the procedures of Sagan and Pollock (JGR, 1967) and Lacis and Hansen (JAS, 1974).
+ follow the procedures of Sagan and Pollock (JGR, 1967) and \cite{lhans:74}.
  Highly accurate heating rate calculations are obtained through the use
  of an optimal grouping strategy of spectral bands.  By grouping the UV and visible regions
-Line 305 
 cloud cover of all the layers in the gro
+Line 308 
 cloud cover of all the layers in the gro
  of a given layer is then scaled for both the direct (as a function of the
  solar zenith angle) and diffuse beam radiation
  so that the grouped layer reflectance is the same as the original reflectance.
- The solar flux is computed for each of the eight cloud realizations possible
+ The solar flux is computed for each of eight cloud realizations possible within this
- (see Figure \ref{fig:fizhi:cloud}) within this
  low/middle/high classification, and appropriately averaged to produce the net solar flux.
- \begin{figure*}[htbp]
-   \vspace{0.4in}
-   \centerline{  \epsfysize=4.0in  %\epsfbox{part6/rhcrit.ps}
-              }
-   \vspace{0.4in}
-   \caption  {Low-Middle-High Cloud Configurations}
-   \label{fig:fizhi:cloud}
- \end{figure*}
  \paragraph{Longwave Radiation}
- The longwave radiation package used in the fizhi package is thoroughly described by Chou and Suarez (1994).
+ The longwave radiation package used in the fizhi package is thoroughly described by \cite{chsz:94}.
  As described in that document, IR fluxes are computed due to absorption by water vapor, carbon
  dioxide, and ozone.  The spectral bands together with their absorbers and parameterization methods,
  configured for the fizhi package, are shown in Table \ref{tab:fizhi:longwave}.
-Line 357 
 Band & Spectral Range (cm$^{-1}$) & Abso
+Line 349 
 Band & Spectral Range (cm$^{-1}$) & Abso
  \end{tabular}
  \end{center}
  \vspace{0.1in}
- \caption{IR Spectral Bands, Absorbers, and Parameterization Method (from Chou and Suarez, 1994)}
+ \caption{IR Spectral Bands, Absorbers, and Parameterization Method (from \cite{chsz:94})}
  \label{tab:fizhi:longwave}
  \end{table}
-Line 417 
 The total optical depth in a given model
+Line 409 
 The total optical depth in a given model
  the large-scale and sub-grid scale optical depths, normalized by the total cloud fraction in the
  layer:
- \[ \tau = \left( {F_{RAS} \,\,\, \tau_{RAS} + F_{LS} \,\,\, \tau_{LS} \over F_{RAS}+F_{LS} } \right) \Delta p, \]
+ \[ \tau = \left( \frac{F_{RAS} \,\,\, \tau_{RAS} + F_{LS} \,\,\, \tau_{LS} }{ F_{RAS}+F_{LS} } \right) \Delta p, \]
  where $F_{RAS}$ and $F_{LS}$ are the time-averaged cloud fractions associated with RAS and large-scale
  processes described in Section \ref{sec:fizhi:clouds}.
-Line 428 
 The cloud fraction values are time-avera
+Line 420 
 The cloud fraction values are time-avera
  hours).  Therefore, in a time-averaged sense, both convective and large-scale
  cloudiness can exist in a given grid-box.
- \subsubsection{Turbulence}
+ \paragraph{Turbulence}:
  Turbulence is parameterized in the fizhi package to account for its contribution to the
  vertical exchange of heat, moisture, and momentum.
  The turbulence scheme is invoked every 30 minutes, and employs a backward-implicit iterative
-Line 458 
 Within the atmosphere, the time evolutio
+Line 451 
 Within the atmosphere, the time evolutio
  of second turbulent moments is explicitly modeled by representing the third moments in terms of
  the first and second moments.  This approach is known as a second-order closure modeling.
  To simplify and streamline the computation of the second moments, the level 2.5 assumption
- of Mellor and Yamada (1974) and Yamada (1977) is employed, in which only the turbulent
+ of Mellor and Yamada (1974) and \cite{yam:77} is employed, in which only the turbulent
  kinetic energy (TKE),
  \[ {\h}{q^2}={\overline{{u^{\prime}}^2}}+{\overline{{v^{\prime}}^2}}+{\overline{{w^{\prime}}^2}}, \]
-Line 470 
 is solved numerically using an implicit
+Line 463 
 is solved numerically using an implicit
  and is written:
  \[
- {\dd{}{t} ({{\h} q^2})} - { \pp{}{z} ({ {5 \over 3} {{\lambda}_1} q { \pp {}{z}
+ {\dd{}{t} ({{\h} q^2})} - { \pp{}{z} ({ \frac{5}{3} {{\lambda}_1} q { \pp {}{z}
  ({\h}q^2)} })} =
  {- \overline{{u^{\prime}}{w^{\prime}}} { \pp{U}{z} }} - {\overline{{v^{\prime}}{w^{\prime}}}
- { \pp{V}{z} }} + {{g \over {\Theta_0}}{\overline{{w^{\prime}}{{{\theta}_v}^{\prime}}}} }
+ { \pp{V}{z} }} + {\frac{g}{\Theta_0}{\overline{{w^{\prime}}{{{\theta}_v}^{\prime}}}}
- - { q^3 \over {{\Lambda} _1} }
+ - \frac{ q^3}{{\Lambda}_1} }
  \]
  where $q$ is the turbulent velocity, ${u^{\prime}}$, ${v^{\prime}}$, ${w^{\prime}}$ and
-Line 492 
 of TKE.
+Line 485 
 of TKE.
  In the level 2.5 approach, the vertical fluxes of the scalars $\theta_v$ and $q$ and the
  wind components $u$ and $v$ are expressed in terms of the diffusion coefficients $K_h$ and
- $K_m$, respectively.  In the statisically realizable level 2.5 turbulence scheme of Helfand
+ $K_m$, respectively.  In the statisically realizable level 2.5 turbulence scheme of
- and Labraga (1988), these diffusion coefficients are expressed as
+ \cite{helflab:88}, these diffusion coefficients are expressed as
  \[
  K_h
   = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) \, & \mbox{decaying turbulence}
- \\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right.
+ \\ \frac{ q^2 }{ q_e } \, \ell \, S_{H}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right.
  \]
  and
-Line 506 
 and
+Line 499 
 and
  \[
  K_m
   = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) \, & \mbox{decaying turbulence}
- \\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right.
+ \\ \frac{ q^2 }{ q_e } \, \ell \, S_{M}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right.
  \]
  where the subscript $e$ refers to the value under conditions of local equillibrium
-Line 518 
 Both $G_H$ and $G_M$, and their equilibr
+Line 511 
 Both $G_H$ and $G_M$, and their equilibr
  are functions of the Richardson number:
  \[
- {\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } }
+ {\bf RI} = \frac{ \frac{g}{\theta_v} \pp{\theta_v}{z} }{ (\pp{u}{z})^2 + (\pp{v}{z})^2 }
-  =  {  {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } .
+  =  \frac{c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} }{ (\pp{u}{z})^2 + (\pp{v}{z})^2 } .
  \]
  Negative values indicate unstable buoyancy and shear, small positive values ($<0.2$)
  indicate dominantly unstable shear, and large positive values indicate dominantly stable
  stratification.
- Turbulent eddy diffusion coefficients of momentum, heat and moisture in the surface layer,
+ Turbulent eddy diffusion coefficients of momentum, heat and moisture in the
- which corresponds to the lowest GCM level (see \ref{tab:fizhi:sigma}),
+ surface layer, which corresponds to the lowest GCM level
+ (see {\it --- missing table ---}%\ref{tab:fizhi:sigma}
+ ),
  are calculated using stability-dependant functions based on Monin-Obukhov theory:
  \[
  {K_m} (surface) = C_u \times u_* = C_D W_s
-Line 543 
 and $W_s$ is the magnitude of the surfac
+Line 538 
 and $W_s$ is the magnitude of the surfac
  $C_u$ is the dimensionless exchange coefficient for momentum from the surface layer
  similarity functions:
  \[
- {C_u} = {u_* \over W_s} = { k \over \psi_{m} }
+ {C_u} = \frac{u_* }{ W_s} = \frac{ k }{ \psi_{m} }
  \]
  where k is the Von Karman constant and $\psi_m$ is the surface layer non-dimensional
  wind shear given by
  \[
- \psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta} .
+ \psi_{m} = {\int_{\zeta_{0}}^{\zeta} \frac{\phi_{m} }{ \zeta} d \zeta} .
  \]
  Here $\zeta$ is the non-dimensional stability parameter, and
  $\phi_m$ is the similarity function of $\zeta$ which expresses the stability dependance of
-Line 558 
 layers.
+Line 553 
 layers.
  $C_t$ is the dimensionless exchange coefficient for heat and
  moisture from the surface layer similarity functions:
  \[
- {C_t} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} =
+ {C_t} = -\frac{( \overline{w^{\prime}\theta^{\prime}}) }{ u_* \Delta \theta } =
- -{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} =
+ -\frac{( \overline{w^{\prime}q^{\prime}}) }{ u_* \Delta q } =
- { k \over { (\psi_{h} + \psi_{g}) } }
+ \frac{ k }{ (\psi_{h} + \psi_{g}) }
  \]
  where $\psi_h$ is the surface layer non-dimensional temperature gradient given by
  \[
- \psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} .
+ \psi_{h} = {\int_{\zeta_{0}}^{\zeta} \frac{\phi_{h} }{ \zeta} d \zeta} .
  \]
  Here $\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of
  the temperature and moisture gradients, and is specified differently for stable and unstable
- layers according to Helfand and Schubert, 1995.
+ layers according to \cite{helfschu:95}.
  $\psi_g$ is the non-dimensional temperature or moisture gradient in the viscous sublayer,
  which is the mosstly laminar region between the surface and the tops of the roughness
  elements, in which temperature and moisture gradients can be quite large.
- Based on Yaglom and Kader (1974):
+ Based on \cite{yagkad:74}:
  \[
- \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} }
+ \psi_{g} = \frac{ 0.55 (Pr^{2/3} - 0.2) }{ \nu^{1/2} }
  (h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2}
  \]
  where Pr is the Prandtl number for air, $\nu$ is the molecular viscosity, $z_{0}$ is the
-Line 584 
 $h_{0} = 30z_{0}$ with a maximum value o
+Line 579 
 $h_{0} = 30z_{0}$ with a maximum value o
  The surface roughness length over oceans is is a function of the surface-stress velocity,
  \[
- {z_0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}}
+ {z_0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + \frac{c_5 }{ u_*}
  \]
  where the constants are chosen to interpolate between the reciprocal relation of
- Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981)
+ \cite{kondo:75} for weak winds, and the piecewise linear relation of \cite{larpond:81}
  for moderate to large winds.  Roughness lengths over land are specified
- from the climatology of Dorman and Sellers (1989).
+ from the climatology of \cite{dorsell:89}.
  For an unstable surface layer, the stability functions, chosen to interpolate between the
  condition of small values of $\beta$ and the convective limit, are the KEYPS function
- (Panofsky, 1973) for momentum, and its generalization for heat and moisture:
+ (\cite{pano:73}) for momentum, and its generalization for heat and moisture:
  \[
  {\phi_m}^4 - 18 \zeta {\phi_m}^3 = 1 \hspace{1cm} ; \hspace{1cm}
  {\phi_h}^2 - 18 \zeta {\phi_h}^3 = 1 \hspace{1cm} .
-Line 602 
 The function for heat and moisture assur
+Line 597 
 The function for heat and moisture assur
  speed approaches zero.
  For a stable surface layer, the stability functions are the observationally
- based functions of Clarke (1970),  slightly modified for
+ based functions of \cite{clarke:70},  slightly modified for
  the momemtum flux:
  \[
- {\phi_m} = { { 1 + 5 {{\zeta}_1} } \over { 1 + 0.00794 {{\zeta}_1}
+ {\phi_m} = \frac{ 1 + 5 {{\zeta}_1} }{ 1 + 0.00794 {\zeta}_1
- (1+ 5 {{\zeta}_1}) } } \hspace{1cm} ; \hspace{1cm}
+ (1+ 5 {\zeta}_1) } \hspace{1cm} ; \hspace{1cm}
- {\phi_h} = { { 1 + 5 {{\zeta}_1} } \over { 1 + 0.00794 {\zeta}
+ {\phi_h} = \frac{ 1 + 5 {{\zeta}_1} }{ 1 + 0.00794 {\zeta}
- (1+ 5 {{\zeta}_1}) } } .
+ (1+ 5 {{\zeta}_1}) } .
  \]
  The moisture flux also depends on a specified evapotranspiration
  coefficient, set to unity over oceans and dependant on the climatological ground wetness over
-Line 653 
 humidity of the surface and of the lowes
+Line 648 
 humidity of the surface and of the lowes
  The heat conduction through sea ice, $Q_{ice}$, is given by
  \[
- {Q_{ice}} = {C_{ti} \over {H_i}} (T_i-T_g)
+ {Q_{ice}} = \frac{C_{ti} }{ H_i} (T_i-T_g)
  \]
  where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to
  be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and $T_g$ is the
  surface temperature of the ice.
  $C_g$ is the total heat capacity of the ground, obtained by solving a heat diffusion equation
- for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by:
+ for the penetration of the diurnal cycle into the ground (\cite{black:77}), and is given by:
  \[
- C_g = \sqrt{ {\lambda C_s \over 2\omega} } = \sqrt{(0.386 + 0.536W + 0.15W^2)2\times10^{-3}
+ C_g = \sqrt{ \frac{\lambda C_s }{ 2\omega} } = \sqrt{(0.386 + 0.536W + 0.15W^2)2\times10^{-3}
- {86400 \over 2 \pi} } \, \, .
+ \frac{86400}{2\pi} } \, \, .
  \]
- Here, the thermal conductivity, $\lambda$, is equal to $2\times10^{-3}$ ${ly\over{ sec}}
+ Here, the thermal conductivity, $\lambda$, is equal to $2\times10^{-3}$ $\frac{ly}{sec}
- {cm \over {^oK}}$,
+ \frac{cm}{K}$,
  the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided
  by $2 \pi$ $radians/
  day$, and the expression for $C_s$, the heat capacity per unit volume at the surface,
  is a function of the ground wetness, $W$.
- \subsubsection{Land Surface Processes}
+ Land Surface Processes:
  \paragraph{Surface Type}
- The fizhi package surface Types are designated using the Koster-Suarez (1992) mosaic
+ The fizhi package surface Types are designated using the Koster-Suarez (\cite{ks:91,ks:92})
- philosophy which allows multiple ``tiles'', or multiple surface types, in any one
+ Land Surface Model (LSM) mosaic philosophy which allows multiple ``tiles'', or multiple surface
- grid cell. The Koster-Suarez Land Surface Model (LSM) surface type classifications
+ types, in any one grid cell. The Koster-Suarez LSM surface type classifications
  are shown in Table \ref{tab:fizhi:surftype}. The surface types and the percent of the grid
  cell occupied by any surface type were derived from the surface classification of
- Defries and Townshend (1994), and information about the location of permanent
+ \cite{deftow:94}, and information about the location of permanent
- ice was obtained from the classifications of Dorman and Sellers (1989).
+ ice was obtained from the classifications of \cite{dorsell:89}.
- The surface type for the \txt GCM grid is shown in Figure \ref{fig:fizhi:surftype}.
+ The surface type map for a $1^\circ$ grid is shown in Figure \ref{fig:fizhi:surftype}.
  The determination of the land or sea category of surface type was made from NCAR's
 minute by 10 minute Navy topography
  dataset, which includes information about the percentage of water-cover at any point.
- The data were averaged to the model's \fxf and \txt grid resolutions,
+ The data were averaged to the model's grid resolutions,
  and any grid-box whose averaged water percentage was $\geq 60 \%$ was
- defined as a water point. The \fxf grid Land-Water designation was further modified
+ defined as a water point. The Land-Water designation was further modified
  subjectively to ensure sufficient representation from small but isolated land and water regions.
  \begin{table}
-Line 712 
 Type & Vegetation Designation \\ \hline
+Line 707 
 Type & Vegetation Designation \\ \hline
 & Ocean \\ \hline
  \end{tabular}
  \end{center}
- \caption{Surface type designations used to compute surface roughness (over land)
+ \caption{Surface type designations.}
- and surface albedo.}
  \label{tab:fizhi:surftype}
  \end{table}
  \begin{figure*}[htbp]
-   \centerline{  \epsfysize=7in  \epsfbox{part6/surftypes.ps}}
+   \centerline{  \epsfysize=4.0in  \epsfbox{s_phys_pkgs/figs/surftype.eps}}
-   \vspace{0.3in}
+   \vspace{0.2in}
-   \caption  {Surface Type Compinations at \txt resolution.}
+   \caption  {Surface Type Combinations.}
    \label{fig:fizhi:surftype}
  \end{figure*}
- \begin{figure*}[htbp]
+ % \rotatebox{270}{\centerline{  \epsfysize=4in  \epsfbox{s_phys_pkgs/figs/surftypes.eps}}}
-   \centerline{  \epsfysize=7in  \epsfbox{part6/surftypes.descrip.ps}}
+ % \rotatebox{270}{\centerline{  \epsfysize=4in  \epsfbox{s_phys_pkgs/figs/surftypes.descrip.eps}}}
-   \vspace{0.3in}
+ %\begin{figure*}[htbp]
-   \caption  {Surface Type Descriptions.}
+ %  \centerline{  \epsfysize=4in  \epsfbox{s_phys_pkgs/figs/surftypes.descrip.ps}}
-   \label{fig:fizhi:surftype.desc}
+ %  \vspace{0.3in}
- \end{figure*}
+ %  \caption  {Surface Type Descriptions.}
+ %  \label{fig:fizhi:surftype.desc}
+ %\end{figure*}
  \paragraph{Surface Roughness}
  The surface roughness length over oceans is computed iteratively with the wind
- stress by the surface layer parameterization (Helfand and Schubert, 1991).
+ stress by the surface layer parameterization (\cite{helfschu:95}).
- It employs an interpolation between the functions of Large and Pond (1981)
+ It employs an interpolation between the functions of \cite{larpond:81}
- for high winds and of Kondo (1975) for weak winds.
+ for high winds and of \cite{kondo:75} for weak winds.
  \paragraph{Albedo}
- The surface albedo computation, described in Koster and Suarez (1991),
+ The surface albedo computation, described in \cite{ks:91},
  employs the ``two stream'' approximation used in Sellers' (1987) Simple Biosphere (SiB)
  Model which distinguishes between the direct and diffuse albedos in the visible
  and in the near infra-red spectral ranges. The albedos are functions of the observed
-Line 750 
 sun), the greenness fraction, the vegeta
+Line 745 
 sun), the greenness fraction, the vegeta
  Modifications are made to account for the presence of snow, and its depth relative
  to the height of the vegetation elements.
- \subsubsection{Gravity Wave Drag}
+ \paragraph{Gravity Wave Drag}
- The fizhi package employs the gravity wave drag scheme of Zhou et al. (1996).
+ The fizhi package employs the gravity wave drag scheme of \cite{zhouetal:95}).
  This scheme is a modified version of Vernekar et al. (1992),
  which was based on Alpert et al. (1988) and Helfand et al. (1987).
  In this version, the gravity wave stress at the surface is
  based on that derived by Pierrehumbert (1986) and is given by:
  \bq
- |\vec{\tau}_{sfc}| = {\rho U^3\over{N \ell^*}} \left(F_r^2 \over{1+F_r^2}\right) \, \, ,
+ |\vec{\tau}_{sfc}| = \frac{\rho U^3}{N \ell^*} \left( \frac{F_r^2}{1+F_r^2}\right) \, \, ,
  \eq
  where $F_r = N h /U$ is the Froude number, $N$ is the {\em Brunt - V\"{a}is\"{a}l\"{a}} frequency, $U$ is the
-Line 768 
 A modification introduced by Zhou et al.
+Line 764 
 A modification introduced by Zhou et al.
  escape through the top of the model, although this effect is small for the current 70-level model.
  The subgrid scale standard deviation is defined by $h$, and is not allowed to exceed 400 m.
- The effects of using this scheme within a GCM are shown in Takacs and Suarez (1996).
+ The effects of using this scheme within a GCM are shown in \cite{taksz:96}.
  Experiments using the gravity wave drag parameterization yielded significant and
  beneficial impacts on both the time-mean flow and the transient statistics of the
  a GCM climatology, and have eliminated most of the worst dynamically driven biases
-Line 784 
 of mountain torque (through a redistribu
+Line 780 
 of mountain torque (through a redistribu
  convergence (through a reduction in the flux of westerly momentum by transient flow eddies).
- \subsubsection{Boundary Conditions and other Input Data}
+ Boundary Conditions and other Input Data:
  Required fields which are not explicitly predicted or diagnosed during model execution must
  either be prescribed internally or obtained from external data sets.  In the fizhi package these
-Line 792 
 fields include:  sea surface temperature
+Line 788 
 fields include:  sea surface temperature
  vegetation index, and the radiation-related background levels of: ozone, carbon dioxide,
  and stratospheric moisture.
- Boundary condition data sets are available at the model's \fxf and \txt
+ Boundary condition data sets are available at the model's
  resolutions for either climatological or yearly varying conditions.
  Any frequency of boundary condition data can be used in the fizhi package;
  however, the current selection of data is summarized in Table \ref{tab:fizhi:bcdata}\@.
  The time mean values are interpolated during each model timestep to the
- current time. Future model versions will incorporate boundary conditions at
+ current time.
- higher spatial \mbox{($1^\circ$ x $1^\circ$)} resolutions.
  \begin{table}[htb]
  \begin{center}
-Line 825 
 current years and frequencies available.
+Line 820 
 current years and frequencies available.
  Surface geopotential heights are provided from an averaging of the Navy 10 minute
  by 10 minute dataset supplied by the National Center for Atmospheric Research (NCAR) to the
  model's grid resolution. The original topography is first rotated to the proper grid-orientation
- which is being run, and then
+ which is being run, and then  averages the data to the model resolution.
- averages the data to the model resolution.
- The averaged topography is then passed through a Lanczos (1966) filter in both dimensions
- which removes the smallest
- scales while inhibiting Gibbs phenomena.
- In one dimension, we may define a cyclic function in $x$ as:
- \begin{equation}
- f(x) = {a_0 \over 2} + \sum_{k=1}^N \left( a_k \cos(kx) + b_k \sin(kx) \right)
- \label{eq:fizhi:filt}
- \end{equation}
- where $N = { {\rm IM} \over 2 }$ and ${\rm IM}$ is the total number of points in the $x$ direction.
- Defining $\Delta x = { 2 \pi \over {\rm IM}}$, we may define the average of $f(x)$ over a
- $2 \Delta x$ region as:
- \begin{equation}
- \overline {f(x)} = {1 \over {2 \Delta x}} \int_{x-\Delta x}^{x+\Delta x} f(x^{\prime}) dx^{\prime}
- \label{eq:fizhi:fave1}
- \end{equation}
- Using equation (\ref{eq:fizhi:filt}) in equation (\ref{eq:fizhi:fave1}) and integrating, we may write:
- \begin{equation}
- \overline {f(x)} = {a_0 \over 2} + {1 \over {2 \Delta x}}
- \sum_{k=1}^N \left [
- \left. a_k { \sin(kx^{\prime}) \over k } \right /_{x-\Delta x}^{x+\Delta x} -
- \left. b_k { \cos(kx^{\prime}) \over k } \right /_{x-\Delta x}^{x+\Delta x}
- \right]
- \end{equation}
- or
- \begin{equation}
- \overline {f(x)} = {a_0 \over 2} + \sum_{k=1}^N {\sin(k \Delta x) \over {k \Delta x}}
- \left( a_k \cos(kx) + b_k \sin(kx) \right)
- \label{eq:fizhi:fave2}
- \end{equation}
- Thus, the Fourier wave amplitudes are simply modified by the Lanczos filter response
- function ${\sin(k\Delta x) \over {k \Delta x}}$.  This may be compared with an $mth$-order
- Shapiro (1970) filter response function, defined as $1-\sin^m({k \Delta x \over 2})$,
- shown in Figure \ref{fig:fizhi:lanczos}.
- It should be noted that negative values in the topography resulting from
- the filtering procedure are {\em not} filled.
- \begin{figure*}[htbp]
-   \centerline{  \epsfysize=7.0in  \epsfbox{part6/lanczos.ps}}
-   \caption{ \label{fig:fizhi:lanczos} Comparison between the Lanczos and $mth$-order Shapiro filter
-   response functions for $m$ = 2, 4, and 8. }
- \end{figure*}
- The standard deviation of the subgrid-scale topography
+ The standard deviation of the subgrid-scale topography is computed by interpolating the 10 minute
- is computed from a modified version of the the Navy 10 minute by 10 minute dataset.
+ data to the model's resolution and re-interpolating back to the 10 minute by 10 minute resolution.
- The 10 minute by 10 minute topography is passed through a wavelet
- filter in both dimensions which removes the scale smaller than 20 minutes.
- The topography is then averaged to $1^\circ x 1^\circ$ grid resolution, and then
- re-interpolated back to the 10 minute by 10 minute resolution.
  The sub-grid scale variance is constructed based on this smoothed dataset.
  \paragraph{Upper Level Moisture}
  The fizhi package uses climatological water vapor data above 100 mb from the Stratospheric Aerosol and Gas
  Experiment (SAGE) as input into the model's radiation packages.  The SAGE data is archived
- as monthly zonal means at 5$^\circ$ latitudinal resolution.  The data is interpolated to the
+ as monthly zonal means at $5^\circ$ latitudinal resolution.  The data is interpolated to the
  model's grid location and current time, and blended with the GCM's moisture data.  Below 300 mb,
  the model's moisture data is used.  Above 100 mb, the SAGE data is used.  Between 100 and 300 mb,
  a linear interpolation (in pressure) is performed using the data from SAGE and the GCM.
- \subsection{Fizhi Diagnostics}
+ \subsubsection{Fizhi Diagnostics}
- \subsubsection{Fizhi Diagnostic Menu}
+ Fizhi Diagnostic Menu:
- \label{sec:fizhi-diagnostics:menu}
+ \label{sec:pkg:fizhi:diagnostics}
  \begin{tabular}{llll}
  \hline\hline
-Line 1424 
 a linear interpolation (in pressure) is
+Line 1367 
 a linear interpolation (in pressure) is
  \newpage
- \subsubsection{Fizhi Diagnostic Description}
+ Fizhi Diagnostic Description:
  In this section we list and describe the diagnostic quantities available within the
  GCM.  The diagnostics are listed in the order that they appear in the
- Diagnostic Menu, Section \ref{sec:fizhi-diagnostics:menu}.
+ Diagnostic Menu, Section \ref{sec:pkg:fizhi:diagnostics}.
  In all cases, each diagnostic as currently archived on the output datasets
  is time-averaged over its diagnostic output frequency:
  \[
- {\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t)
+ {\bf DIAGNOSTIC} = \frac{1}{TTOT} \sum_{t=1}^{t=TTOT} diag(t)
  \]
- where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the
+ where $TTOT = \frac{ {\bf NQDIAG} }{\Delta t}$, {\bf NQDIAG} is the
  output frequency of the diagnostic, and $\Delta t$ is
  the timestep over which the diagnostic is updated.
-Line 1507 
 conduction from the relatively warm ocea
+Line 1450 
 conduction from the relatively warm ocea
  through sea ice represents an additional energy source term for the ground temperature equation.
  \[
- {\bf QICE} = {C_{ti} \over {H_i}} (T_i-T_g)
+ {\bf QICE} = \frac{C_{ti}}{H_i} (T_i-T_g)
  \]
  where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to
-Line 1549 
 the downward Shortwave flux and $F_{SW}^
+Line 1492 
 the downward Shortwave flux and $F_{SW}^
  \noindent
  The non-dimensional stability indicator is the ratio of the buoyancy to the shear:
  \[
- {\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } }
+ {\bf RI} = \frac{ \frac{g}{\theta_v} \pp {\theta_v}{z} }{ (\pp{u}{z})^2 + (\pp{v}{z})^2 }
-  =  {  {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } }
+  =  \frac{c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} }{ (\pp{u}{z})^2 + (\pp{v}{z})^2 }
  \]
  \\
  where we used the hydrostatic equation:
-Line 1569 
 stratification.
+Line 1512 
 stratification.
  The surface exchange coefficient is obtained from the similarity functions for the stability
   dependant flux profile relationships:
  \[
- {\bf CT} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} =
+ {\bf CT} = -\frac{( \overline{w^{\prime}\theta^{\prime}} ) }{ u_* \Delta \theta } =
- -{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} =
+ -\frac{( \overline{w^{\prime}q^{\prime}} ) }{ u_* \Delta q } =
- { k \over { (\psi_{h} + \psi_{g}) } }
+ \frac{ k }{ (\psi_{h} + \psi_{g}) }
  \]
  where $\psi_h$ is the surface layer non-dimensional temperature change and $\psi_g$ is the
  viscous sublayer non-dimensional temperature or moisture change:
  \[
- \psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} \hspace{1cm} and
+ \psi_{h} = \int_{\zeta_{0}}^{\zeta} \frac{\phi_{h} }{ \zeta} d \zeta \hspace{1cm} and
- \hspace{1cm} \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} }
+ \hspace{1cm} \psi_{g} = \frac{ 0.55 (Pr^{2/3} - 0.2) }{ \nu^{1/2} }
  (h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2}
  \]
  and:
-Line 1586 
 $h_{0} = 30z_{0}$ with a maximum value o
+Line 1529 
 $h_{0} = 30z_{0}$ with a maximum value o
  \noindent
  $\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of
  the temperature and moisture gradients, specified differently for stable and unstable
- layers according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the
+ layers according to \cite{helfschu:95}. k is the Von Karman constant, $\zeta$ is the
  non-dimensional stability parameter, Pr is the Prandtl number for air, $\nu$ is the molecular
  viscosity, $z_{0}$ is the surface roughness length, $u_*$ is the surface stress velocity
  (see diagnostic number 67), and the subscript ref refers to a reference value.
-Line 1599 
 viscosity, $z_{0}$ is the surface roughn
+Line 1542 
 viscosity, $z_{0}$ is the surface roughn
  The surface exchange coefficient is obtained from the similarity functions for the stability
   dependant flux profile relationships:
  \[
- {\bf CU} = {u_* \over W_s} = { k \over \psi_{m} }
+ {\bf CU} = \frac{u_* }{ W_s} = \frac{ k }{ \psi_{m} }
  \]
  where $\psi_m$ is the surface layer non-dimensional wind shear:
  \[
- \psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta}
+ \psi_{m} = {\int_{\zeta_{0}}^{\zeta} \frac{\phi_{m} }{ \zeta} d \zeta}
  \]
  \noindent
  $\phi_m$ is the similarity function of $\zeta$, which expresses the stability dependance of
  the temperature and moisture gradients, specified differently for stable and unstable layers
- according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the
+ according to \cite{helfschu:95}. k is the Von Karman constant, $\zeta$ is the
  non-dimensional stability parameter, $u_*$ is the surface stress velocity
  (see diagnostic number 67), and $W_s$ is the magnitude of the surface layer wind.
  \\
-Line 1620 
 non-dimensional stability parameter, $u_
+Line 1563 
 non-dimensional stability parameter, $u_
  In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat or
  moisture flux for the atmosphere above the surface layer can be expressed as a turbulent
  diffusion coefficient $K_h$ times the negative of the gradient of potential temperature
- or moisture. In the Helfand and Labraga (1988) adaptation of this closure, $K_h$
+ or moisture. In the \cite{helflab:88} adaptation of this closure, $K_h$
  takes the form:
  \[
- {\bf ET} = K_h = -{( {\overline{w^{\prime}\theta_v^{\prime}}}) \over {\pp{\theta_v}{z}} }
+ {\bf ET} = K_h = -\frac{( \overline{w^{\prime}\theta_v^{\prime}}) }{ \pp{\theta_v}{z} }
   = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) & \mbox{decaying turbulence}
- \\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right.
+ \\ \frac{ q^2 }{ q_e } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right.
  \]
  where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm}
  energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model,
-Line 1639 
 are functions of the Richardson number.
+Line 1582 
 are functions of the Richardson number.
  \noindent
  For the detailed equations and derivations of the modified level 2.5 closure scheme,
- see Helfand and Labraga, 1988.
+ see \cite{helflab:88}.
  \noindent
  In the surface layer, ${\bf {ET}}$ is the exchange coefficient for heat and moisture,
-Line 1661 
 and $W_s$ is the magnitude of the surfac
+Line 1604 
 and $W_s$ is the magnitude of the surfac
  In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat
  momentum flux for the atmosphere above the surface layer can be expressed as a turbulent
  diffusion coefficient $K_m$ times the negative of the gradient of the u-wind.
- In the Helfand and Labraga (1988) adaptation of this closure, $K_m$
+ In the \cite{helflab:88} adaptation of this closure, $K_m$
  takes the form:
  \[
- {\bf EU} = K_m = -{( {\overline{u^{\prime}w^{\prime}}}) \over {\pp{U}{z}} }
+ {\bf EU} = K_m = -\frac{( \overline{u^{\prime}w^{\prime}} ) }{ \pp{U}{z} }
   = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) & \mbox{decaying turbulence}
- \\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right.
+ \\ \frac{ q^2 }{ q_e } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right.
  \]
  \noindent
  where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm}
-Line 1681 
 are functions of the Richardson number.
+Line 1624 
 are functions of the Richardson number.
  \noindent
  For the detailed equations and derivations of the modified level 2.5 closure scheme,
- see Helfand and Labraga, 1988.
+ see \cite{helflab:88}.
  \noindent
  In the surface layer, ${\bf {EU}}$ is the exchange coefficient for momentum,
-Line 1769 
 equation.
+Line 1712 
 equation.
  \]
  where:
  \[
- \left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over c_p} \Gamma_s \right)_i
+ \left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha \frac{m_B}{c_p} \Gamma_s \right)_i
  \hspace{.4cm} and
- \hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = {L \over c_p } (q^*-q)
+ \hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = \frac{L}{c_p} (q^*-q)
  \]
  and
  \[
-Line 1799 
 $R$ is the rain re-evaporation adjustmen
+Line 1742 
 $R$ is the rain re-evaporation adjustmen
  \]
  where:
  \[
- \left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over {L}}(\Gamma_h-\Gamma_s) \right)_i
+ \left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha \frac{m_B}{L}(\Gamma_h-\Gamma_s) \right)_i
  \hspace{.4cm} and
  \hspace{.4cm} \left.{\pp{q}{t}}\right|_{ls} = (q^*-q)
  \]
-Line 1845 
 F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}
+Line 1788 
 F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}
  Finally, the net longwave heating rate is calculated as the vertical divergence of the
  net terrestrial radiative fluxes:
  \[
- \pp{\rho c_p T}{t} = - {\partial \over \partial z} F_{LW}^{NET} ,
+ \pp{\rho c_p T}{t} = - \p{z} F_{LW}^{NET} ,
  \]
  or
  \[
- {\bf RADLW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F_{LW}^{NET} .
+ {\bf RADLW} = \frac{g}{c_p \pi} \p{\sigma} F_{LW}^{NET} .
  \]
  \noindent
-Line 1880 
 input at the top of the atmosphere.
+Line 1823 
 input at the top of the atmosphere.
  \noindent
  The heating rate due to Shortwave Radiation under cloudy skies is defined as:
  \[
- \pp{\rho c_p T}{t} = - {\partial \over \partial z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT},
+ \pp{\rho c_p T}{t} = - \p{z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT},
  \]
  or
  \[
- {\bf RADSW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} .
+ {\bf RADSW} = \frac{g}{c_p \pi} \p{\sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} .
  \]
  \noindent
-Line 1904 
 For a change in specific humidity due to
+Line 1847 
 For a change in specific humidity due to
  the vertical integral or total precipitable amount is given by:
  \[
  {\bf PREACC} = \int_{surf}^{top} \rho \Delta q_{moist} dz = - \int_{surf}^{top} \Delta  q_{moist}
- {dp \over g} = {1 \over g} \int_0^1 \Delta q_{moist} dp
+ \frac{dp}{g} = \frac{1}{g} \int_0^1 \Delta q_{moist} dp
  \]
  \\
-Line 1921 
 For a change in specific humidity due to
+Line 1864 
 For a change in specific humidity due to
  the vertical integral or total precipitable amount is given by:
  \[
  {\bf PRECON} = \int_{surf}^{top} \rho \Delta q_{cum} dz = - \int_{surf}^{top} \Delta  q_{cum}
- {dp \over g} = {1 \over g} \int_0^1 \Delta q_{cum} dp
+ \frac{dp}{g} = \frac{1}{g} \int_0^1 \Delta q_{cum} dp
  \]
  \\
-Line 2006 
 where $\rho$ is the air density, and $K_
+Line 1949 
 where $\rho$ is the air density, and $K_
  \noindent
  The drag coefficient for momentum obtained by assuming a neutrally stable surface layer:
  \[
- {\bf CN} = { k \over { \ln({h \over {z_0}})} }
+ {\bf CN} = \frac{ k }{ \ln(\frac{h }{z_0}) }
  \]
  \noindent
-Line 2042 
 The air/surface virtual temperature diff
+Line 1985 
 The air/surface virtual temperature diff
  \noindent
  where
  \[
- \theta_{v{Nrphys+1}} = { T_g \over {P^{\kappa}_{surf}} } (1 + .609 q_{Nrphys+1}) \hspace{1cm}
+ \theta_{v{Nrphys+1}} = \frac{ T_g }{ P^{\kappa}_{surf} } (1 + .609 q_{Nrphys+1}) \hspace{1cm}
  and \hspace{1cm} q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys})
  \]
-Line 2071 
 net surface upward longwave radiative fl
+Line 2014 
 net surface upward longwave radiative fl
  sea ice, $H$ is the upward sensible heat flux, $LE$ is the upward latent heat
  flux, and $C_g$ is the total heat capacity of the ground.
  $C_g$ is obtained by solving a heat diffusion equation
- for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by:
+ for the penetration of the diurnal cycle into the ground (\cite{black:77}), and is given by:
  \[
- C_g = \sqrt{ {\lambda C_s \over {2 \omega} } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3}
+ C_g = \sqrt{ \frac{\lambda C_s }{ 2 \omega } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3}
- { 86400. \over {2 \pi} } } \, \, .
+ \frac{86400.}{2\pi} } \, \, .
  \]
  \noindent
- Here, the thermal conductivity, $\lambda$, is equal to $2x10^{-3}$ ${ly\over{ sec}}
+ Here, the thermal conductivity, $\lambda$, is equal to $2x10^{-3}$ $\frac{ly}{sec}
- {cm \over {^oK}}$,
+ \frac{cm}{K}$,
  the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided
  by $2 \pi$ $radians/
  day$, and the expression for $C_s$, the heat capacity per unit volume at the surface,
-Line 2220 
 Thus, {\bf LWCLR} is defined as the net
+Line 2163 
 Thus, {\bf LWCLR} is defined as the net
  vertical divergence of the
  clear-sky longwave radiative flux:
  \[
- \pp{\rho c_p T}{t}_{clearsky} = - {\partial \over \partial z} F(clearsky)_{LW}^{NET} ,
+ \pp{\rho c_p T}{t}_{clearsky} = - \p{z} F(clearsky)_{LW}^{NET} ,
  \]
  or
  \[
- {\bf LWCLR} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(clearsky)_{LW}^{NET} .
+ {\bf LWCLR} = \frac{g}{c_p \pi} \p{\sigma} F(clearsky)_{LW}^{NET} .
  \]
  \noindent
-Line 2414 
 The surface stress velocity, or the fric
+Line 2357 
 The surface stress velocity, or the fric
  the surface layer top impeded by the surface drag:
  \[
  {\bf USTAR} = C_uW_s \hspace{1cm}where: \hspace{.2cm}
- C_u = {k \over {\psi_m} }
+ C_u = \frac{k}{\psi_m}
  \]
  \noindent
-Line 2426 
 number 10), and $W_s$ is the surface win
+Line 2369 
 number 10), and $W_s$ is the surface win
  \noindent
  Over the land surface, the surface roughness length is interpolated to the local
- time from the monthly mean data of Dorman and Sellers (1989). Over the ocean,
+ time from the monthly mean data of \cite{dorsell:89}. Over the ocean,
  the roughness length is a function of the surface-stress velocity, $u_*$.
  \[
- {\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}}
+ {\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5}{u_*}
  \]
  \noindent
  where the constants are chosen to interpolate between the reciprocal relation of
- Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981)
+ \cite{kondo:75} for weak winds, and the piecewise linear relation of \cite{larpond:81}
  for moderate to large winds.
  \\
-Line 2483 
 input at the top of the atmosphere.
+Line 2426 
 input at the top of the atmosphere.
  \noindent
  The heating rate due to Shortwave Radiation under clear skies is defined as:
  \[
- \pp{\rho c_p T}{t} = - {\partial \over \partial z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT},
+ \pp{\rho c_p T}{t} = - \p{z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT},
  \]
  or
  \[
- {\bf SWCLR} = \frac{g}{c_p } {\partial \over \partial p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} .
+ {\bf SWCLR} = \frac{g}{c_p } \p{p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} .
  \]
  \noindent
-Line 2674 
 If we define the time-tendency of Temper
+Line 2617 
 If we define the time-tendency of Temper
  \end{eqnarray*}
  then, since there are no surface pressure changes due to Diabatic processes, we may write
  \[
- \pp{T}{t}_{Diabatic} = {p^\kappa \over \pi }\pp{\pi \theta}{t}_{Diabatic}
+ \pp{T}{t}_{Diabatic} = \frac{p^\kappa}{\pi}\pp{\pi \theta}{t}_{Diabatic}
  \]
  where $\theta = T/p^\kappa$.  Thus, {\bf DIABT} may be written as
  \[
- {\bf DIABT} = {p^\kappa \over \pi } \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right)
+ {\bf DIABT} = \frac{p^\kappa}{\pi} \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right)
  \]
  \\
-Line 2697 
 If we define the time-tendency of Specif
+Line 2640 
 If we define the time-tendency of Specif
  \]
  then, since there are no surface pressure changes due to Diabatic processes, we may write
  \[
- \pp{q}{t}_{Diabatic} = {1 \over \pi }\pp{\pi q}{t}_{Diabatic}
+ \pp{q}{t}_{Diabatic} = \frac{1}{\pi}\pp{\pi q}{t}_{Diabatic}
  \]
  Thus, {\bf DIABQ} may be written as
  \[
- {\bf DIABQ} = {1 \over \pi } \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right)
+ {\bf DIABQ} = \frac{1}{\pi} \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right)
  \]
  \\
-Line 2715 
 and dividing by the total mass of the co
+Line 2658 
 and dividing by the total mass of the co
  \[
  {\bf VINTUQ} = \frac{ \int_{surf}^{top} u q \rho dz  } { \int_{surf}^{top} \rho dz  }
  \]
- Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have
+ Using $\rho \delta z = -\frac{\delta p}{g} = - \frac{1}{g} \delta p$, we have
  \[
  {\bf VINTUQ} = { \int_0^1 u q dp  }
  \]
-Line 2732 
 and dividing by the total mass of the co
+Line 2675 
 and dividing by the total mass of the co
  \[
  {\bf VINTVQ} = \frac{ \int_{surf}^{top} v q \rho dz  } { \int_{surf}^{top} \rho dz  }
  \]
- Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have
+ Using $\rho \delta z = -\frac{\delta p}{g} = - \frac{1}{g} \delta p$, we have
  \[
  {\bf VINTVQ} = { \int_0^1 v q dp  }
  \]
-Line 2765 
 and dividing by the total mass of the co
+Line 2708 
 and dividing by the total mass of the co
  \[
  {\bf VINTVT} = \frac{ \int_{surf}^{top} v T \rho dz  } { \int_{surf}^{top} \rho dz  }
  \]
- Using $\rho \delta z = -{\delta p \over g} $, we have
+ Using $\rho \delta z = -\frac{\delta p}{g} $, we have
  \[
  {\bf VINTVT} = { \int_0^1 v T dp  }
  \]
-Line 2830 
 The Total Precipitable Water is defined
+Line 2773 
 The Total Precipitable Water is defined
  given by:
  \begin{eqnarray*}
  {\bf QINT} & = & \int_{surf}^{top} \rho q dz \\
-            & = & {\pi \over g} \int_0^1 q dp
+            & = & \frac{\pi}{g} \int_0^1 q dp
  \end{eqnarray*}
  where we have used the hydrostatic relation
- $\rho \delta z = -{\delta p \over g} $.
+ $\rho \delta z = -\frac{\delta p}{g} $.
  \\
-Line 2843 
 $\rho \delta z = -{\delta p \over g} $.
+Line 2786 
 $\rho \delta z = -{\delta p \over g} $.
  \noindent
  The u-wind at the 2-meter depth is determined from the similarity theory:
  \[
- {\bf U2M} = {u_* \over k} \psi_{m_{2m}} {u_{sl} \over {W_s}} =
+ {\bf U2M} = \frac{u_*}{k} \psi_{m_{2m}} \frac{u_{sl}}{W_s} =
- { \psi_{m_{2m}} \over {\psi_{m_{sl}} }}u_{sl}
+ \frac{ \psi_{m_{2m}} }{ \psi_{m_{sl}} }u_{sl}
  \]
  \noindent
-Line 2859 
 is above two meters, ${\bf U2M}$ is unde
+Line 2802 
 is above two meters, ${\bf U2M}$ is unde
  \noindent
  The v-wind at the 2-meter depth is a determined from the similarity theory:
  \[
- {\bf V2M} = {u_* \over k} \psi_{m_{2m}} {v_{sl} \over {W_s}} =
+ {\bf V2M} = \frac{u_*}{k} \psi_{m_{2m}} \frac{v_{sl}}{W_s} =
- { \psi_{m_{2m}} \over {\psi_{m_{sl}} }}v_{sl}
+ \frac{ \psi_{m_{2m}} }{ \psi_{m_{sl}} }v_{sl}
  \]
  \noindent
-Line 2875 
 is above two meters, ${\bf V2M}$ is unde
+Line 2818 
 is above two meters, ${\bf V2M}$ is unde
  \noindent
  The temperature at the 2-meter depth is a determined from the similarity theory:
  \[
- {\bf T2M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) =
+ {\bf T2M} = P^{\kappa} (\frac{\theta*}{k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) =
- P^{\kappa}(\theta_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }
+ P^{\kappa}(\theta_{surf} + \frac{ \psi_{h_{2m}}+\psi_g }{ \psi_{h_{sl}}+\psi_g }
- (\theta_{sl} - \theta_{surf}))
+ (\theta_{sl} - \theta_{surf}) )
  \]
  where:
  \[
- \theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} }
+ \theta_* = - \frac{ (\overline{w^{\prime}\theta^{\prime}}) }{ u_* }
  \]
  \noindent
-Line 2897 
 is above two meters, ${\bf T2M}$ is unde
+Line 2840 
 is above two meters, ${\bf T2M}$ is unde
  \noindent
  The specific humidity at the 2-meter depth is determined from the similarity theory:
  \[
- {\bf Q2M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) =
+ {\bf Q2M} = P^{\kappa} \frac({q_*}{k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) =
- P^{\kappa}(q_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }
+ P^{\kappa}(q_{surf} + \frac{ \psi_{h_{2m}}+\psi_g }{ \psi_{h_{sl}}+\psi_g }
  (q_{sl} - q_{surf}))
  \]
  where:
  \[
- q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} }
+ q_* = - \frac{ (\overline{w^{\prime}q^{\prime}}) }{ u_* }
  \]
  \noindent
-Line 2921 
 The u-wind at the 10-meter depth is an i
+Line 2864 
 The u-wind at the 10-meter depth is an i
  and the model lowest level wind using the ratio of the non-dimensional wind shear
  at the two levels:
  \[
- {\bf U10M} = {u_* \over k} \psi_{m_{10m}} {u_{sl} \over {W_s}} =
+ {\bf U10M} = \frac{u_*}{k} \psi_{m_{10m}} \frac{u_{sl}}{W_s} =
- { \psi_{m_{10m}} \over {\psi_{m_{sl}} }}u_{sl}
+ \frac{ \psi_{m_{10m}} }{ \psi_{m_{sl}} }u_{sl}
  \]
  \noindent
-Line 2938 
 The v-wind at the 10-meter depth is an i
+Line 2881 
 The v-wind at the 10-meter depth is an i
  and the model lowest level wind using the ratio of the non-dimensional wind shear
  at the two levels:
  \[
- {\bf V10M} = {u_* \over k} \psi_{m_{10m}} {v_{sl} \over {W_s}} =
+ {\bf V10M} = \frac{u_*}{k} \psi_{m_{10m}} \frac{v_{sl}}{W_s} =
- { \psi_{m_{10m}} \over {\psi_{m_{sl}} }}v_{sl}
+ \frac{ \psi_{m_{10m}} }{ \psi_{m_{sl}} }v_{sl}
  \]
  \noindent
-Line 2955 
 The temperature at the 10-meter depth is
+Line 2898 
 The temperature at the 10-meter depth is
  temperature and the model lowest level potential temperature using the ratio of the
  non-dimensional temperature gradient at the two levels:
  \[
- {\bf T10M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) =
+ {\bf T10M} = P^{\kappa} (\frac{\theta*}{k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) =
- P^{\kappa}(\theta_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }
+ P^{\kappa}(\theta_{surf} + \frac{\psi_{h_{10m}}+\psi_g}{\psi_{h_{sl}}+\psi_g}
  (\theta_{sl} - \theta_{surf}))
  \]
  where:
  \[
- \theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} }
+ \theta_* = - \frac{ (\overline{w^{\prime}\theta^{\prime}}) }{ u_* }
  \]
  \noindent
-Line 2978 
 The specific humidity at the 10-meter de
+Line 2921 
 The specific humidity at the 10-meter de
  humidity and the model lowest level specific humidity using the ratio of the
  non-dimensional temperature gradient at the two levels:
  \[
- {\bf Q10M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) =
+ {\bf Q10M} = P^{\kappa} (\frac{q_*}{k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) =
- P^{\kappa}(q_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} }
+ P^{\kappa}(q_{surf} + \frac{\psi_{h_{10m}}+\psi_g}{\psi_{h_{sl}}+\psi_g}
  (q_{sl} - q_{surf}))
  \]
  where:
  \[
- q_* =  - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} }
+ q_* =  - \frac{ (\overline{w^{\prime}q^{\prime}}) }{ u_* }
  \]
  \noindent
-Line 3025 
 q^{n+1} = (\pi q)^{n+1} / \pi^{n+1}
+Line 2968 
 q^{n+1} = (\pi q)^{n+1} / \pi^{n+1}
  \]
- \subsection{Key subroutines, parameters and files}
+ \subsubsection{Key subroutines, parameters and files}
+ \subsubsection{Dos and donts}
+ \subsubsection{Fizhi Reference}
+ \subsubsection{Experiments and tutorials that use fizhi}
+ \label{sec:pkg:fizhi:experiments}
- \subsection{Dos and donts}
+ \begin{itemize}
+ \item{Global atmosphere experiment with realistic SST and topography in fizhi-cs-32x32x10 verification directory. }
+ \item{Global atmosphere aqua planet experiment in fizhi-cs-aqualev20 verification directory. }
+ \end{itemize}
- \subsection{Fizhi Reference}

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